Novel Approach to the Reconstruction of Partially Detected Evolving Systems

This thesis focuses on the study of evolving systems for which a sequence of exact but partial observations is being made. I present a novel strategy — SIS with corrections — to infer the state of the system and impute the missing data under Bayesian models. The strategy involves simulating multiple alternative states consistent with current knowledge of the system, as revealed by the observations. However, a difficult problem that arises is that observations made later are invariably incompatible with previously simulated states. To solve this problem, I propose a two-step iterative process in which states of the system are alternately simulated in accordance with past observations, then corrected in light of new observations.